(Parts of the following section may not be prior art.)
Fiber lasers with high pulse energy, good beam quality and excellent optical characteristics have applications in many fields and industries such as materials processing (marking, welding, semiconductor wafer and mask repair etc), medical and industrial spectroscopy (fluorescence, absorption), illumination, remote sensing and spectroscopy (wind speed, biohazards, ecosystem mapping etc), ranging and targeting (collision avoidance, military applications etc) and scientific instrumentation. For reasons of simplicity and efficiency, Yb3+-doped fibers are most commonly used. They can be optically pumped from 915 nm-975 nm and achieve emission from 975-1100 nm with optical conversion efficiency as high as 70%. Currently, advances in this field are primarily constrained by limitations in maximum extractable energy, and the onset of nonlinear impairments. Saturation energy of the gain medium is a key parameter for determining how much energy can be stored in an amplifier, and is given byi 
                              E          sat                =                                            hv              s                        ⁢                          A              eff                                                          (                                                σ                  es                                +                                  σ                  as                                            )                        ⁢                          Γ              s                                                          (        1        )            where σes,σas are the emission and absorption cross section at the signal wavelength, hνs is signal energy at frequency νs, Aeff is area of the active doped region and Γs is signal overlap with the active dopant. As a general rule, the extractable energy stored in a fiber is limited to around ten times the saturation energy. As an example, for standard single mode Yb3+ doped fiber with 8 μm core diameter, Esat=0.04 mJ, indicating extraction of only about 0.4 mJ per pulse.
Two deleterious nonlinear effects of concern are stimulated Brillouin scattering (SBS) and stimulated Raman scattering (SRS). Both rob power from the signal and can cause catastrophic damage. For SRS, the threshold for peak power Pth before onset of serious Raman scattering in passive fibers is given by:
                              P          th                =                              16            ⁢                          A              eff                                                          g              R                        ⁢            L                                              (        2        )            where Aeff is the effective mode area of the fiber, gR is the Raman gain coefficient and L is the fiber length. For a fiber with 25 μm core diameter, Pth·L˜70 kWm. Since typical fiber lengths exceed 5 meters, this indicates peak powers of only 20 kW before Raman scattering becomes severe.
Stimulated Brillouin scattering arises from interaction of the signal with longitudinal acoustic modes of the fiber, causing part of the signal to be reflected backwards. Similar to the case of SRS, the threshold condition for SBS can be written as:
                              P          th                =                                            21              ⁢                              A                eff                                                                    g                B                            ⁢              L                                ⁢                      (                          1              +                              BW                                  BW                                      SiO                    2                                                                        )                                              (        3        )            where gB is the Brillouin gain coefficient, BW is the bandwidth of the signal and BWSiO2 is the Brillouin bandwidth of a silica, i.e. SiO2, fiber (˜50 MHz for silica). If the signal has bandwidth comparable to BWSiO2, then for a fiber with 25 μm core diameter, Pth·L˜350 Wm. This is obviously a severe constraint and mitigation is desirable.
For both SBS and SRS impairments, equations (3) and (4) indicate mitigation is possible by increasing the modal area and decreasing the fiber length. Because a larger core occupies a larger fraction of the overall fiber cross-section and therefore has higher pump absorption, the optimum fiber length varies inversely with Aeff. Thus, increasing the core area naturally results in shorter length. Since the nonlinear effects vary as A/L, the increase in threshold varies as Aeff2.
Currently, the practical solution for obtaining large Aeff fiber is conceptually straightforward—simply increasing the core diameter. This results in monotonically increasing Aeff of the signal. However, there are several limitations to this approach. For single-mode operation, as the core diameter increases, the refractive index difference between the core and cladding, Δn, must decrease. If Δn<0.001, though, the fiber becomes bend sensitive. And when Δn is fixed at a minimum, further increase in core diameter results in multimode operation. While this is permissible, core size is then constrained by unavoidable but undesirable energy transfer among modes.
The mode coupling efficiency η between modes in a multimode fiber is given by
                    η        ∼                                            λ              2                        ⁢                          κ              2                                            Δ            ⁢                                                  ⁢                          n              eff                              2                ⁢                p                                                                        (        4        )            where κ is the perturbation amplitude due to index and microbend fluctuations, Δneff is the difference in effective indices between different modes, and p is a fitting parameter (with value >0) to account for mechanical perturbations on a fiber. Thus, large Δneff (e.g. >8×10−5) is desirable for low mode coupling. Unfortunately, as Aeff increases, Δneff decreases and rapidly asymptotes to values much smaller than 8×10−4, and mode coupling cannot be reduced. This is illustrated in FIG. 1, which shows simulations of two designs for achieving Aeff˜1600 μm2 (mode field ˜45 μm). FIG. 1a shows the refractive index profiles of the designs considered. The fiber with higher Δn has Δneff=6×10−5, indicating that it is highly susceptible to mode coupling. Note that this mode has negligible bend loss, as shown in FIG. 1b. Even with a huge reduction in Δn, Δneff is only increased by 30% and mode coupling remains catastrophic. Note that this reduction in Δn leads to extreme bend loss (FIG. 1b).
FIG. 1c illustrates an additional problem with large Aeff designs. All applications of high power lasers and amplifiers involve spatially transforming and focusing the device output. This is best achieved with Gaussian beams. Thus, an important metric for high power devices is the M2 of the output light, where M2 is a measure of the departure from a perfect Gaussian spatial profile (M2=1 is a perfectly Gaussian mode), given by:
                              M          2                =                              ∫                                          r                2                            ⁢                              E                2                            ⁢                              r                ·                                  ⅆ                  r                                                                          ∫                                                            (                                                            ⅆ                      E                                        /                                          ⅆ                      r                                                        )                                2                            ⁢                              r                ·                                  ⅆ                  r                                                                                        (        5        )            where E is the electric field profile of the mode, and r is the radial coordinate. FIG. 1c shows two mode profiles representing two different M2 values for the two different designs (low and high mode coupling) represented in FIG. 1a. The output beam, becomes highly distorted (M2 dramatically increases) for the design with low mode coupling, and is sensitive to index perturbations in the core. Very tight control of fiber fabrication conditions is therefore necessary to maintain good beam quality, and this is difficult in fibers with Aeff>350 μm2.
Current preferred laser designs concentrate on means to force operation in a fundamental mode, even though the fiber may guide several modes. One disclosed means to achieve this is to preferentially strip the higher order modes (HOM). While this may be adequate for moderate Aeff, the higher modal content of large Aeff fibers leaves little room for discrimination of bend loss between modes. Alternatively, gain-inducing dopants can be selectively deposited in a fiber preform so that only the fundamental mode is substantially amplified or guided. While this technique would allow amplification of the desired mode in comparison to HOMs, it is designed for cases where the fundamental mode is substantially spatially separated from the HOMs—a condition typically absent in very large Aeff fibers. Another approach is to dope the fiber in a ring around the core rather than in the core itself. This increases the gain saturation limit of the gain medium, allowing extraction of higher power pulses. However, this technique leads to significant degradation of the output mode profile, i.e. departure from M2=1. Since many of the HOMs overlap spatially, mode coupling and mode discrimination becomes problematic.
Given the numerous performance trade-offs, gain fibers with current technology face a practical limit of mode field diameter ˜20 μm (Aeff=350 μm2) with little prospect of future advances using conventional engineering expedients. Thus there exists a need for an amplifier fiber that simultaneously yields very large Aeff, low mode coupling, and good output beam quality.